(a) Find the number N such that when (frac{1}{3}) of it is added to 8, the result is the same as when (frac{1}{2}) of it is subtracted from 18.
(b) Using a ruler and a pair of compasses only, construct a trapezium ABCD, in which the parallel sides AB and DC are 4 cm apart. < DAB = 60°, /AB/ = 8 cm and /BC/ = 5 cm. Measure /DC/.
Explanation
(a) Let the number be N.
(frac{N}{3} + 8 = 18 – frac{N}{2})
(frac{N}{3} + frac{N}{2} = 18 – 8 = 10)
(frac{5N}{6} = 10 implies 5N = 60)
(N = 12)
(b)